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# HW4 - Physics 121 Problem Set 4 due Friday April 30 1...

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Unformatted text preview: Physics 121 - Problem Set # 4 due Friday, April 30 1. Griﬃths, problem 9.16 2. Griﬃths, problem 9.20 3. Consider an elastic string with mass density ρ and tension κ. The string is coated in the interval 0 < z < so that the mass density increases to ρ2 in this interval. The tension κ remains constant throughout the string. (a) By imposing the condition that both f (z ) and ∂f /∂z are continuous at both boundaries, ﬁnd a solution to the wave equation of the form: Re f0 [eikz −iωt + Re−ikz −iωt ] , z<0 ik2 z −iωt −ik2 z −iωt f (z, t) = Re f0 [Ae + Be ], 0 < z < ikz −iωt Re f0 [T e ], <z (b) Show from the explicit solution that 1 = |R|2 + |T |2 . Why? (c) Plot |R|2 and |T |2 as a function of (k /2π ) for the case ρ2 /ρ = 4. Explain the qualitative behavior. In particular, what happens when (k /2π ) = 1/2? 4. Griﬃths, problem 9.34. Note that the previous problem was a warm-up for this one. 5. Griﬃths, problem 9.35 1 ...
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